A114603 Decimal expansion of constant appearing in asymptotic variance of estimator for Pi in the Buffon-Laplace needle problem on a triangular grid with l/d=1.

0, 1, 5, 7, 6, 5, 8, 6, 3, 7, 3, 0, 3, 0, 4, 4, 2, 1, 6, 6, 7, 5, 6, 4, 9, 9, 4, 6, 5, 1, 1, 1, 7, 1, 8, 5, 3, 4, 3, 9, 7, 4, 1, 3, 8, 3, 7, 7, 2, 2, 4, 6, 0, 9, 4, 3, 3, 6, 0, 3, 6, 0, 0, 6, 9, 6, 8, 8, 4, 9, 8, 3, 5, 1, 0, 6, 2, 8, 6, 2, 2, 5, 8, 2, 0, 9, 9, 6, 5, 1, 0, 9, 5, 4, 4, 0, 0, 8, 8, 7, 8, 0, 0

Offset

0,3

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's World of Mathematics, Buffon-Laplace Needle Problem

Formula

(2*(3*sqrt(3) - 4*Pi)*(3*sqrt(3) - Pi)*Pi^2*(-8 + sqrt(3) + 2*Pi)*(-24 + 3*sqrt(3) + 5*Pi))/(3*(-3618 + 864*sqrt(3) + 828*Pi + 354*sqrt(3)*Pi - 269*Pi^2 + 32*sqrt(3)*Pi^2)).

Example

0.0157658637...

Mathematica

RealDigits[(2*(3*Sqrt[3] - 4*Pi)*(3*Sqrt[3] - Pi)*Pi^2*(-8 + Sqrt[3] + 2*Pi)*(-24 + 3*Sqrt[3] + 5*Pi))/(3*(-3618 + 864*Sqrt[3] + 828*Pi + 354*Sqrt[3]*Pi - 269*Pi^2 + 32*Sqrt[3]*Pi^2)), 10, 100][[1]] (* Vaclav Kotesovec, Aug 15 2015 after Eric W. Weisstein *)

Crossrefs

Sequence in context: A198730 A318733 A195444 * A348731 A346590 A100554

Adjacent sequences: A114600 A114601 A114602 * A114604 A114605 A114606

Keyword

nonn,cons,easy

Author

Eric W. Weisstein, Dec 14 2005

Status

approved